Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 59, 2011 - Issue 6
250
Views
29
CrossRef citations to date
0
Altmetric
Original Articles

Phase Change Problems Using the MLPG Method

, &
Pages 438-458 | Received 09 Jul 2010, Accepted 10 Dec 2010, Published online: 03 Mar 2011

REFERENCES

  • H. S. Carslaw and J. C. Jaeger , Conduction of Heat in Solids, , 2nd ed. , Clarendon Press , Oxford , 1959 .
  • K. A. Rathjen and L. M. Jiji , Heat Conduction with Melting or Freezing in a Corner , ASME J. Heat Transfer , vol. 93 , pp. 101 – 109 , 1971 .
  • H. Budhia and F. Kreith , Heat transfer with Melting or Freezing in a Wedge , Int. J. Heat and Mass Transfer , vol. 16 , pp. 195 – 211 , 1973 .
  • L. M. Jiji , Heat Conduction, , 3rd ed. , Begell House , New York , USA , 2009 .
  • S. Del Giudice , G. Comini , and R.W. Lewis , Finite Element Simulation of Freezing Processes in Soils , Int. J. Numer. and Analytical Method in Geomechanics , vol. 2 , pp. 223 – 235 , 1978 .
  • E. G. Lemmon , Phase Change Techniques for Finite Element Codes , in R. W. Lewis and K. Morgan (eds.) , Numerical Methods in Thermal Problems (Proc. Conf.) , Pineridge Press , Swansea , pp. 149 – 158 , 1979 .
  • Q. T. Pham , The Use of Lumped Capacitance in the Finite Element Solution of Heat Conduction Problems with Phase Change , Int. J. Heat and Mass Transfer , vol. 29 , pp. 285 – 291 , 1986 .
  • A. J. Dalhuijsen and A. Segal , Comparison of Finite Element Techniques for Solidification Problems , Int. J. for Numer. Methods in Eng. , vol. 23 , pp. 1807 – 1829 , 1986 .
  • D. Celentano , E. Onate , and S. Oller , A Temperature-Based Formulation for Finite Element Analysis of Generalized Phase-Change Problems , Int. J. for Numer. Methods in Eng. , vol. 37 , pp. 3441 – 3465 , 1994 .
  • T. Ouyang and K. K. Tamma , Finite Element Simulations Involving Simultaneous Multiple Interface Fronts in Phase Change Problems , Int. J. Heat and Mass Transfer , vol. 39 , pp. 1711 – 1718 , 1996 .
  • K. N. Seetharamu , R. Paragsam , G. A. Quadir , Z. A. Zainal , B. S. Prasad , and T. Sundararajan , Finite element Modeling of Solidification Phenomena , Sadhana-Academy Proc. in Eng. Sci. , vol. 26 , pp. 103 – 120 , 2001 .
  • L. E. Goodrich , Efficient Numerical Technique for One-Dimentional Thermal Problems with Phase Change , Int. J. Heat and Mass Transfer , vol. 21 , pp. 615 – 621 , 1978 .
  • G. Comini , S. D. Guidice , and O. Saro , A Conservative Algorithm for Multidimensional Conduction Phase Change , Int. J. Numer. Methods in Eng. , vol. 30 , pp. 697 – 709 , 1990 .
  • R. L. McAdie , J. T. Cross , R. W. Lewis , and D. T. Gethin , A Finite Element Enthalpy Technique for Solving Coupled Nonlinear Heat Conduction , Int. J. Numer. Method in Heat and Fluid Flow , vol. 5 , pp. 907 – 921 , 1995 .
  • M. Bhattacharya , T. Basak , and K. G. Ayappa , A Fixed-Grid Finite Element Based Enthalpy Formulation for Generalized Phase Change Problems: Role of Superficial Mushy Region , Int. J. Heat and Mass Transfer , vol. 45 , pp. 4881 – 4898 , 2002 .
  • B. Nedjar , An Enthalpy-Based Finite Element Method for Nonlinear Heat Transfer Problems Involving Phase Change , Computers and Structures , vol. 80 , pp. 9 – 21 , 2002 .
  • E. Feulvarch and J. M. Bergheau , An Implicit Fixed-Grid Method for the Finite Element Analysis of Heat Transfer Involving Phase Changes , Numer. Heat Transfer, Part B , vol. 51 , pp. 585 – 610 , 2007 .
  • E. Feulvarch , J. M. Bergheau , and J. B. Leblond , An Implicit Finite Element Algorithm for the Simulation of Diffusion with Phase Changes in Solids , Int. J. Numer. Method in Eng. , vol. 78 , pp. 1492 – 1512 , 2009 .
  • G. Vidalain , L. Gosselin , and M. Lacroix , An Enhanced Thermal Conduction Model for the Prediction of Convection Dominated Solid-Liquid Phase Change, Int. J. Heat and Mass Transfer , vol. 52, pp. 1753–1760, 2009.
  • Y. Liu , H. Zhang , and M.-W. Lu , A Meshless based Method on Least-Square Approach for Steady and Unsteady State Heat Conduction Problems , Numer. Heat Transfer B , vol. 47 , pp. 257 – 275 , 2005 .
  • H. Sadat , N. Dubus , L. Gbahoue , and T. Sophy , On the Solution of Heterogeneous Heat Conduction by a Diffuse Approximation Meshless Method , Numer. Heat Transfer B , vol. 50 , pp. 491 – 498 , 2006 .
  • A. Singh , I. V. Singh , and R. Prakash , Temperature-Dependent Thermal Conductivity Problems Using Meshless Method , Numer. Heat Transfer A , vol. 50 , pp. 125 – 145 , 2006 .
  • A. Singh , I. V. Singh , and R. Prakash , Meshless Analysis of Unsteady-State Heat Transfer in Semi-Infinite Solids with Temperature-Dependent Thermal Conductivity , Int. Comm. in Heat and Mass Transfer , vol. 33 , pp. 231 – 239 , 2006 .
  • A. Singh , I. V. Singh , and R. Prakash , Meshless Element free Galerkin Method for Unsteady Nonlinear Heat Transfer problems , Int. J. Heat and Mass Transfer , vol. 50 , pp. 1212 – 1219 , 2007 .
  • J. Y. Tan , J. M. Zhao , and L. H. Liu , Meshless Method for Geometry Identification Problem of Heat Conduction , Numer. Heat Transfer B , vol. 55 , pp. 135 – 154 , 2009 .
  • J. Fang , G.–F. Zhao , J. Zhao , and A. Parriaux , On the Truly Meshless Solution of Heat Conduction Problems in Heterogeneous Media , Numer. Heat Transfer B , vol. 55 , pp. 1 – 13 , 2009 .
  • R. C. Batra , M. Porfiri , and D. Spinello , Treatment of Material Discontinuity in Two Meshless Local Petrov-Galerkin (MLPG) Formulations of Axisymmetric Transient Heat Conduction , Int. J. Numer. Methods in Eng. , vol. 61 , pp. 2461 – 2479 , 2004 .
  • A. Arefmanesh , M. Najafi , and H. Abdi , A Meshless Local Petrov-Galerkin Method for Fluid Dynamics and Heat Transfer , ASME J. Fluid Eng. , vol. 127 , pp. 647 – 655 , 2005 .
  • J. Sladek , V. Sladek , and Y. C. Hon , Inverse Heat Conduction Problems by Meshless Local Petrov-Galerkin Method , Eng. Analysis with Boundary Elements , vol. 30 , pp. 650 – 661 , 2006 .
  • X.-H. Wu and W.-Q. Tao , Meshless Method Based on the Local Weak-Forms for Steady-State Heat Conduction Problems , Int. J. Heat and Mass Transfer , vol. 51 , pp. 3103 – 3112 , 2008 .
  • M. Sterk and R. Trobec , Meshless Solution of a Diffusion Equation with Parameter Optimization and Error Analysis , Eng. Analysis with Boundary Elements , vol. 32 , pp. 567 – 577 , 2008 .
  • H. C. Thakur , K. M. Singh , and P. K. Sahoo , Meshless Local Petrov-Galerkin Method for Nonlinear Heat Conduction Problems , Numer. Heat Transfer B , vol. 56 , pp. 393 – 410 , 2009 .
  • R. Vertnik and B. Sarler , Meshless Local Radial Basis Function Collocation Method for Convective-Diffusive Solid-Liquid Phase Change Problems , Int. J. Numer. Methods for Heat and Fluid Flow , vol. 16 , pp. 617 – 640 , 2006 .
  • R. Vertnik , M. Zaloznik , and B. Sarler , Solution of Transient Direct-Chill Aluminum Billet Casting Problem with Simultaneous Material and Interface Moving Boundaries by a Meshless Method , Eng. Analysis with Boundary Elements , vol. 30 , pp. 847 – 855 , 2006 .
  • Z. Gao , Y. Lai , M. Zhang , J. Qi , and S. Zhang , Element Free Galerkin Method for Nonlinear Heat Transfer with Phase Change in Qinghai-Tibet Railway Embankment , Cold Regions Sci. and Tech. , vol. 48 , pp. 15 – 23 , 2007 .
  • L. Zhang , H.-F. Shen , Y. Rong , and T.-Y. Huang , Numerical Simulation on Solidification and Thermal Stress of Continuous Casting Billet in Mold based on Meshless Methods , Material Sci. Eng. , vol. 466 , pp. 71 – 78 , 2007 .
  • H. Yang and Y. He , Solving Heat Transfer with Phase Change via Smoothed Heat Capacity and Element-Free Galerkin Methods, Int. Comm. Heat and Mass Transfer , vol. 37, pp. 385–392, 2010.
  • S. N. Atluri and T. Zhu , A New Meshless Local Petrov–Galerkin (MLPG) Approach in Computational Mechanics , Computational Mech. , vol. 22 , pp. 117 – 127 , 1998 .
  • S. N. Atluri and T. Zhu , A New Meshless Local Petrov–Galerkin (MLPG) Approach to Nonlinear Problems in Computational Modeling and Simulation , Computational Modeling and Simulation in Eng. , vol. 3 , pp. 187 – 196 , 1998 .
  • P. Lancaster and K. Salkauskas , Surfaces Generated by Moving Least Squares Methods , Mathematical Computation , vol. 37 , pp. 141 – 158 , 1981 .
  • R. W. Lewis and P. M. Roberts , Finite Element Simulation of Solidification Problems , Appl. Scientific Res. , vol. 44 , pp. 61 – 92 , 1987 .
  • H. Thakur , Meshless Local Petrov-Galerkin Method for Phase Change Problems, Ph.D. Thesis, Indian Institute of Roorkee , Roorkee , India , 2010 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.